Here is one way to write the same letter three times: n + n + n. Is there a neater way to write three of the same letter added together?

Think of each x as a bag with an unknown number of cubes inside, and each plain number as loose cubes on the table.

Watch three expressions get tidied up. Each board is captioned with the algebra it is showing, so you can see the bags and the expression at the same time.

Key point Only like terms can be combined. Bags join with bags because they hold the same unknown amount. Loose numbers join with loose numbers. A bag and a loose number are not like terms, so they can never be pushed together into one term.

Before each answer appears, predict which terms are alike and which have to stay apart.

Sort the scattered cards into two groups. Put the x-bags (the x-terms) in one place. Put the loose cubes (the plain numbers) in the other. The cards on screen are 5x, 2, 3x, x and 4. When they are sorted, say the simplified expression aloud.

Sort every card into its group: x-terms with x-terms, plain numbers with plain numbers. Only like terms go together.

When the cards are sorted, say the whole simplified expression out loud and write it in your copy. Both parts, so 7x + 3, not just 7x. The board checks the sorting; you supply the expression.

The sets get harder: two x-terms and one number, then two x-terms and two numbers, then three x-terms and two numbers. Predict how many x-bags and how many loose cubes each set will end with before you press Check.